IST Lunch Bunch

We study games in which each player can simultaneously exert costlyeffort to provides different benefits to some of the other players.The static analysis of the game yields a prediction of no cooperation,while a standard repeated games approach yields a folk theorem inwhich anything goes. To obtain more refined predictions about repeatedplay, we start from the observation that outcomes in such settings aretypically negotiated in multilateral meetings involving varioussubsets of players. Thus, our goal is to find and describe effortprofiles that can be sustained in equilibrium despite the possibilityof coordinated coalitional deviations.

In general, even the existence of such solutions is a difficultmatter. This paper argues that there are simple, efficient, andcoalition-proof equilibria that can be found by analyzing the settingas a network of marginal benefit flows among players. In theseequilibria each player's effort is equal to a sum (appropriatelyweighted) of the efforts of those whose contributions help him at themargin; this is an eigenvector centrality condition in the network. Toestablish the main result, we study connections among three concepts:coalition-proof equilibria of a repeated game; Lindahl equilibria(which are "market" solutions in a static public goods environment);and effort profiles satisfying the centrality condition. We also finda simple spectral characterization of Pareto-efficient outcomes of ourpublic goods environment: they are the ones where a certain marginalbenefits matrix has a largest eigenvalue of 1.